While I agree that Charleston is THE place to go, Columbia is a great second choice. In addition to the Zoo and Five Points, I would recommend the following:
1. Take a tour of the USC campus. Very pretty up on the old horseshoe.
2. Tour the state capitol building and grounds. Lots of history there including still visible holes where Union cannonballs hit.
3. Go to the Vista for some night life and antique stores.
4. Tour the historic buildings and churches immediately surrounding the capital.
I know some folks don't like Columbia, but I have had some of the best weeks of my life in that town.
In this photo, don't forget to ask how Washington's cane was broken and WHY it has not been repaired.